Pyramidal Height of Small Stellated Dodecahedron given Total Surface Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*(sqrt(Total Surface Area of Small Stellated Dodecahedron/(15*(sqrt(5+2*sqrt(5))))))
hPyramid = ((sqrt(25+10*sqrt(5)))/5)*(sqrt(TSA/(15*(sqrt(5+2*sqrt(5))))))
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Pyramidal Height of Small Stellated Dodecahedron - (Measured in Meter) - Pyramidal Height of Small Stellated Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Small Stellated Dodecahedron.
Total Surface Area of Small Stellated Dodecahedron - (Measured in Square Meter) - Total Surface Area of Small Stellated Dodecahedron is the total quantity of plane enclosed by the entire surface of the Small Stellated Dodecahedron.
STEP 1: Convert Input(s) to Base Unit
Total Surface Area of Small Stellated Dodecahedron: 4600 Square Meter --> 4600 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
hPyramid = ((sqrt(25+10*sqrt(5)))/5)*(sqrt(TSA/(15*(sqrt(5+2*sqrt(5)))))) --> ((sqrt(25+10*sqrt(5)))/5)*(sqrt(4600/(15*(sqrt(5+2*sqrt(5))))))
Evaluating ... ...
hPyramid = 13.7391626484325
STEP 3: Convert Result to Output's Unit
13.7391626484325 Meter --> No Conversion Required
FINAL ANSWER
13.7391626484325 13.73916 Meter <-- Pyramidal Height of Small Stellated Dodecahedron
(Calculation completed in 00.004 seconds)

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Walchand College of Engineering (WCE), Sangli
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7 Pyramidal Height of Small Stellated Dodecahedron Calculators

Pyramidal Height of Small Stellated Dodecahedron given Surface to Volume Ratio
Go Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*SA:V of Small Stellated Dodecahedron))
Pyramidal Height of Small Stellated Dodecahedron given Total Surface Area
Go Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*(sqrt(Total Surface Area of Small Stellated Dodecahedron/(15*(sqrt(5+2*sqrt(5))))))
Pyramidal Height of Small Stellated Dodecahedron given Circumradius
Go Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5))))
Pyramidal Height of Small Stellated Dodecahedron given Volume
Go Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*(((4*Volume of Small Stellated Dodecahedron)/(5*(7+3*sqrt(5))))^(1/3))
Pyramidal Height of Small Stellated Dodecahedron given Ridge Length
Go Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*((2*Ridge Length of Small Stellated Dodecahedron)/(1+sqrt(5)))
Pyramidal Height of Small Stellated Dodecahedron given Pentagram Chord
Go Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*(Pentagram Chord of Small Stellated Dodecahedron/(2+sqrt(5)))
Pyramidal Height of Small Stellated Dodecahedron
Go Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*Edge Length of Small Stellated Dodecahedron

Pyramidal Height of Small Stellated Dodecahedron given Total Surface Area Formula

Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*(sqrt(Total Surface Area of Small Stellated Dodecahedron/(15*(sqrt(5+2*sqrt(5))))))
hPyramid = ((sqrt(25+10*sqrt(5)))/5)*(sqrt(TSA/(15*(sqrt(5+2*sqrt(5))))))

What is Small Stellated Dodecahedron?

The Small Stellated Dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol {5⁄2,5}. It is one of four nonconvex regular polyhedra. It is composed of 12 pentagrammic faces, with five pentagrams meeting at each vertex.

How to Calculate Pyramidal Height of Small Stellated Dodecahedron given Total Surface Area?

Pyramidal Height of Small Stellated Dodecahedron given Total Surface Area calculator uses Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*(sqrt(Total Surface Area of Small Stellated Dodecahedron/(15*(sqrt(5+2*sqrt(5)))))) to calculate the Pyramidal Height of Small Stellated Dodecahedron, Pyramidal Height of Small Stellated Dodecahedron given Total Surface Area formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Small Stellated Dodecahedron, calculated using its total surface area. Pyramidal Height of Small Stellated Dodecahedron is denoted by hPyramid symbol.

How to calculate Pyramidal Height of Small Stellated Dodecahedron given Total Surface Area using this online calculator? To use this online calculator for Pyramidal Height of Small Stellated Dodecahedron given Total Surface Area, enter Total Surface Area of Small Stellated Dodecahedron (TSA) and hit the calculate button. Here is how the Pyramidal Height of Small Stellated Dodecahedron given Total Surface Area calculation can be explained with given input values -> 13.73916 = ((sqrt(25+10*sqrt(5)))/5)*(sqrt(4600/(15*(sqrt(5+2*sqrt(5)))))).

FAQ

What is Pyramidal Height of Small Stellated Dodecahedron given Total Surface Area?
Pyramidal Height of Small Stellated Dodecahedron given Total Surface Area formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Small Stellated Dodecahedron, calculated using its total surface area and is represented as hPyramid = ((sqrt(25+10*sqrt(5)))/5)*(sqrt(TSA/(15*(sqrt(5+2*sqrt(5)))))) or Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*(sqrt(Total Surface Area of Small Stellated Dodecahedron/(15*(sqrt(5+2*sqrt(5)))))). Total Surface Area of Small Stellated Dodecahedron is the total quantity of plane enclosed by the entire surface of the Small Stellated Dodecahedron.
How to calculate Pyramidal Height of Small Stellated Dodecahedron given Total Surface Area?
Pyramidal Height of Small Stellated Dodecahedron given Total Surface Area formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Small Stellated Dodecahedron, calculated using its total surface area is calculated using Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*(sqrt(Total Surface Area of Small Stellated Dodecahedron/(15*(sqrt(5+2*sqrt(5)))))). To calculate Pyramidal Height of Small Stellated Dodecahedron given Total Surface Area, you need Total Surface Area of Small Stellated Dodecahedron (TSA). With our tool, you need to enter the respective value for Total Surface Area of Small Stellated Dodecahedron and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Pyramidal Height of Small Stellated Dodecahedron?
In this formula, Pyramidal Height of Small Stellated Dodecahedron uses Total Surface Area of Small Stellated Dodecahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*Edge Length of Small Stellated Dodecahedron
  • Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*((2*Ridge Length of Small Stellated Dodecahedron)/(1+sqrt(5)))
  • Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*(Pentagram Chord of Small Stellated Dodecahedron/(2+sqrt(5)))
  • Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5))))
  • Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*(((4*Volume of Small Stellated Dodecahedron)/(5*(7+3*sqrt(5))))^(1/3))
  • Pyramidal Height of Small Stellated Dodecahedron = ((sqrt(25+10*sqrt(5)))/5)*((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*SA:V of Small Stellated Dodecahedron))
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